Numerical experiments on the Calogero lattice

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Abstract
This paper presents the results of computer experiments performed on one‐dimensional, classical mechanical, N‐body systems whose point particles interact pairwise via the potential V (r) =ar2+br−2, where r is interparticle distance and where a and b are positive constants. When each particle interacts with all other particles, the numerical experiments indicate that the system is mathematically integrable for either free‐end or fixed‐end boundary conditions. On the other hand, when each particle interacts with only its nearest neighbors, the computer detects a transition from near‐integrable to stochastic behavior again for either free‐end or fixed‐end boundary conditions. Our results thus support the conjecture that integrability is highly sensitive to changes in the total interaction potential but insensitive to modification of boundary conditions.